I've read the marketing hype about the X-E2 with its "fast" autofocus. Also, the new price point of $1399 with an f/2.8 zoom seems very appealing. This test was only done in the store and here are my impressions:

autofocus stinks! The E-M1 is so much better. The ability to focus on a nearest object or face doesn't exist in the fuji (it's one or the other). The fuji has no touch screen and thus tap to focus isn't and option. Facial autofocus missed the mark quite often.

No 3.5mm audio jack.

The lenses do not feel solid in comparison to canons lenses

live view on my 5d3 with quick focus mode is every bit as fast as the fuji and it's full frame.

Noisy lenses and sluggish focusing.

Glad I chose the E-M1 for my mirrorless camera. In the meantime, I tried the panasonic 25mm f/1.4 which I'm sorry I did. Why? I ended up buying it.

Own both Fuji XE2 and Olympus OMD (albeit EM5). the autofocus on XE2 may not feel faster than on OMD but it is very accurate. Also the image quality on XE2 is being compared by MANY these days to full frame cameras image quality.

conclusion: While I’m not including any side by side comparison shots from the 5D Mark III and the Fuji X-E2, suffice to say that I have not found a single instance where the quality of the X-E2 was such that I could really tell the difference between the 2 cameras.”

In conclusion, XE2 image quality is remarkable for a crop camera. And it is a small camera with addictive personality and intuitive controls. Another great thing about Fuji X is ability to shoot straight JPEGS, they are insanely good and give you a lot of room for recovery in highlights/shadows and I am talking about JPEGS. In fact, this is the only camera I own that I started to shoot straight JPEGS.

But if all you care about is AF speed and face recognition, then yes, Olympus is much better. Ability to focus on the nearest eye is quite helpful for me in catching my 19-month-old child who runs nonstop in any direction and never stops.